World Academy of Science, Engineering and Technology
International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering Vol:2, No:6, 2008
Voltage Stability Investigation of
Grid Connected Wind Farm
International Science Index, Electrical and Computer Engineering Vol:2, No:6, 2008 waset.org/Publication/14898
Trinh Trong Chuong
Abstract—At present, it is very common to find renewable
energy resources, especially wind power, connected to distribution
systems. The impact of this wind power on voltage distribution levels
has been addressed in the literature. The majority of this works deals
with the determination of the maximum active and reactive power
that is possible to be connected on a system load bus, until the
voltage at that bus reaches the voltage collapse point. It is done by the
traditional methods of PV curves reported in many references.
Theoretical expression of maximum power limited by voltage
stability transfer through a grid is formulated using an exact
representation of distribution line with ABCD parameters. The
expression is used to plot PV curves at various power factors of a
radial system. Limited values of reactive power can be obtained. This
paper presents a method to study the relationship between the active
power and voltage (PV) at the load bus to identify the voltage
stability limit. It is a foundation to build a permitted working
operation region in complying with the voltage stability limit at the
point of common coupling (PCC) connected wind farm.
The existence of voltage dips is one of the main
disturbances related to power quality in distribution networks.
In developed countries, it is known that from 75% up to 95%
of the industrial sector claims to the electric distribution
companies are related to problems originated by this
disturbance type [4, 5]. These problems arise from the fact that
many electrical loads are not designed to maintain their
normal use behaviour during a voltage dip. The aim of this
paper is to conduct a voltage stability analysis using exact
representation of distribution line with ABCD parameters, to
evaluate the impact of strategically placed wind generators on
distribution systems with respect to the critical voltage
variations and collapse margins. This paper concludes with the
discussion of wind generators excellent options for voltage
stability [1].
Keywords—Wind generator, Voltage stability, grid connected
Induction machines are use extensively in the power system
as induction motors but are not widely used as generators.
Despite their simplicity in construction, they are not preferred
as much as synchronous generators. This is mainly due to the
defined relationship between the export of P and absorption of
Q. However, induction generators have the benefits of
providing large damping torque in the prime mover, which
makes it suitable for the application in fixed speed WTs. The
fixed speed WT uses a squirrel cage induction generator that is
coupled to the power system through a connecting transformer
as shown in Fig 1 [1]. Due to different operating speeds of the
WT rotor and generator, a gearbox is used to match these
speeds. The generator slip slightly varies with the amount of
generated power and is therefore not entirely constant [4].
I. INTRODUCTION.
R
ECENTLY Wind Generator (WG) has been experiencing
a rapid development in a global scale. The size of wind
turbines and wind farms are increasing quickly; a large
amount of wind power is integrated into the power system. As
the wind power penetration into the grid increases quickly, the
influence of wind turbines (WT) on the power quality and
voltage stability is becoming more and more important..
Highlight a section that you want to designate with a certain
style, then select the appropriate name on the style menu. The
style will adjust your fonts and line spacing. It is well known
that a huge penetration of wind energy in a power system may
cause important problems due to the random nature of the
wind and the characteristics of the wind generators.
II. INDUCTION MACHINES
Wind turbine
gearbox
In large wind farms connected to the transmission network
the main technical constraint to take into account is the power
system transient stability that could be lost when, for example,
a voltage dip causes the switch off of a large number of WGs.
In the case of smaller installations connected to weak electric
grids, power quality problems may became a serious concern
because of the proximity of the generators to the loads.
Trinh Trong Chuong is with the Department: Electric Power System, Hanoi
University of Industry, Vietnam. Email: chuonghtd@gmail.com. Tel:
(+84)0904993611
International Scholarly and Scientific Research & Innovation 2(6) 2008
G
Induction
Generator
PG r QG
vG
iG
Grid
Fig. 1 Modelling wind turbine connected grid [1]
However, because these speed variations are in the order of
1 per cent this wind turbine is normally referred to as constant
speed. Nowadays, this type of wind turbine is nearly always
combined with stall control of the aerodynamic power,
although pitch-controlled constant speed wind turbine types
have been built in the past. Induction machines consume
reactive power and consequently, it is present practice to
provide power factor correction capacitors at each WT. These
are typically rated at around 30 percent of the wind
farmcapacity. As the stator voltage of most wind turbine
electrical generators is 690V, the connecting transformer of
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scholar.waset.org/1999.5/14898
World Academy of Science, Engineering and Technology
International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering Vol:2, No:6, 2008
the wind turbine is essential for connection to the distribution
network and should be considered when modeling the
electrical interaction with the power system [2].
International Science Index, Electrical and Computer Engineering Vol:2, No:6, 2008 waset.org/Publication/14898
III. VOLTAGE STABILTY
A system experiences a state of voltage instability when
there is a progressive or uncontrollable drop in voltage
magnitude after a disturbance, increase in load demand or
change in operating condition. The main factor, which causes
these unacceptable voltage profiles, is the inability of the
distribution system to meet the demand for reactive power.
Under normal operating conditions, the bus voltage magnitude
(V) increases as Q injected at the same bus is increased.
However, when V of any one of the system’s buses decreases
with the increase in Q for that same bus, the system is said to
be unstable. Although the voltage instability is a localised
problem, its impact on the system can be wide spread as it
depends on the relationship between transmitted P, injected Q
and receiving end V. These relationships play an important
role in the stability analysis, can be displayed graphically [1].
which is usually generated by a series of load flow solutions.
Figure 3 shows a voltage stability limit at the point where the
derivative dQ/dV is zero. This point also defines the minimum
reactive power requirement for a stable operation. An increase
in Q will result an increase in voltage during normal operating
conditions. Hence, if the operating point is on the right side of
the curve, the system is said to be stable. Conversely,
operating points in the left side of the graph are deemed to be
unstable [4, 5].
IV. VOLTAGE STABILITY BOUNDARY
If the WG produces Pgen + jQgen ; local load is Pload + jQload,
the complex power delivered to the line shown in Fig 4 is:
S line
PWT
(1)
From the phasor diagram in figure 5 the per-unit voltage rise
at the local busbar may be estimated as:
'U
R.Pgrid X .Qgrid
U grid
III.1. PV Curves
When considering voltage stability, the relationship between
transmitted P and receiving end V is of interest. The voltage
stability analysis process involves the transfer of P from one
region of a system to another, and monitoring the effects to the
system voltages, V. This type of analysis is commonly
referred to as a PV study.
PL j QWT QL U
S
X .Pgrid R.Qgrid
ŀ‘ G
AB
CD
A
A‘D
B
B‘ E
(2)
U grid
2
1
System
j
U L ‘0
ŀ
WT
ŀ
Wind
turbine
Loads
Fig. 4 Radial feeder with connected WG
Fig. 2 Charactic P-V
Fig. 3 Charatic Q-V
The Fig 2 shows a typical PV curve. It represents the
variation in voltage at a particular bus as a function of the total
active power supplied to loads or sinking areas. It can be seen
that at the “knee” of the PV curve, the voltage drops rapidly
when there is an increase in the load demand. Load flow
solutions do not converge beyond this point, which indicates
that the system has become unstable. This point is called the
Critical point. Hence, the curve can be used to determine the
system’s critical operating voltage and collapse margin.
Generally, operating points above the critical point signifies a
stable system. If the operating points are below the critical
point, the system is diagnosed to be in an unstable condition
[5].
III.2. QV curves
Voltage stability depends on how the variations in Q and P
affect the voltages at the load buses. The influence of reactive
power characteristics of devices at the receiving end is more
apparent in a QV relationship.It shows the sensitivity and
variation of bus voltages with respect to reactive power
injections or absorptions. Fig 3 shows a typical QV curve,
International Scholarly and Scientific Research & Innovation 2(6) 2008
Fig. 5 Voltage Phasor Diagram
MVAR
UL
P
E-D
O
T
G
'
MW
C'
U L2
Z
I
I'
G
C
T
U S .U L
Z
Fig. 6 UPCD for short distribution line
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scholar.waset.org/1999.5/14898
World Academy of Science, Engineering and Technology
International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering Vol:2, No:6, 2008
Equations 1 and 2 show that, where line power flow is
dominated by WG production, operating asynchronous WGs
at a constant power factor will result in voltage excursion as
the plant tries to export reactive power in constant proportion
to active power. Line impedance directly increases voltage
rise. Line X/R ratio skews the effects of real and reactive
power. A clearer appreciation of these may be obtained by
considering the Universal Power Circle Diagram (UPCD) for
a short distribution line shown in Fig 6 [1], [11].
International Science Index, Electrical and Computer Engineering Vol:2, No:6, 2008 waset.org/Publication/14898
A radial transmission line is shown in Fig. 4 in which a
generator with a constant voltage US‘į supplying complex
power SL to a load with a terminal voltage UL‘0 through a
transmission line represented by its ABCD parameters.
Complex power at the receiving end of a transmission line
shown in Fig. 4 is given as [4,8]:
SL
U U
AU L2
‘E D S L ‘E G
B
B
(3)
The above equation (3) represents a circle for varying value
AU L2
of į with position of centre indicated by
‘E D and
B
U U
radius by S L where A = A ‘Į and B = B ‘ȕ are the line
B
G th'
SL
Therefore: S L
'
For SL to be maximum: dS L
dG
'
U S2
4 A.B. sin 2 I ' / 2
@
(13)
S L max . cos I
QL lim
S L max . sin I
(14)
Receiving end voltage is obtained as:
UL
U S . sin I ' G '
A. sin I '
(15)
Caculator Zth; I; I'
Calculator: SLmax, Gth, ULth
change 'G
Power and Voltage at PCC with
references of cosI
0
(8)
End
'
(9)
Fig. 7 Flow chart
(10)
Solution of (9) provides critical value of power angle į,
critical value of voltage and maximum value of complex
power:
S L max
Contruction P - V curves
dS L
dG '
> S Lmax sin I ' G ' sin G '
cos 2 I ' / 2
(7)
U sin I G sin G
AB sin 2 I '
2
S
(12)
(5)
U S2 sin T sin G '
AB sin 2 I '
D ;
US
2 A. sin I ' / 2
PL max
(6)
1800 I ' G '
2
The maximum value of active power and limiting value of
reactive power:
(4)
OC
sin T
Also from ǻOCP: T
2
I
Equation (9), (11) and (12) relate complex power with
maximum complex power:
I is the power factor angle and is positive for lagging power
factor and negative for leading power factor. In ǻOCP:
From (3) to (6): S L
90 0 Input data
U SU L
AU L2
OC
CP
; OP S L ;
B
B
'
0
'
I 180 E D I ;
G G D
CP
sin I '
I ' and
G th
Therefore : U Lth
constants and į is power angle. From Fig. 6:
OP
sin G '
90 0 (11)
International Scholarly and Scientific Research & Innovation 2(6) 2008
This limits dispatch of complex power. While these
diagrams are based on complex power flow in the line, they
are useful to visualise the effects of network changes on the
limits of operation and dispatch of asynchronous WGs
connected to the local busbar, particularly where the capacity
of the WG is dominant. They also enable computation and
examination of loci of busbar voltage as the WG is loaded or
as local demand varies, while the plant is in constant power
factor or constant voltage control, the flow chart is shown in
Fig. 7.
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World Academy of Science, Engineering and Technology
International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering Vol:2, No:6, 2008
V. TEST SYSTEM
The studied model represents an equivalent of the Phuoc
Ninh, Ninh Thuan, Viet Nam (Fig. 8) system in the area where
large scale wind power production is located [6, 10]. The
model represents a 50 MW wind power station consisting 50
turbines with fixed speed asynchronous generators directly
connected to the grid. The turbines are stall regulated type,
with a rating of 1.0 MW each. Fig 9 shows the equivalent
model of the system. Zth = (0,00125 +j0.005) [11]. Sending
end voltage is constant.
U, kV
0.7
0.6
0.5
0.4
0.3
0.2
0.1
P, MW
0
10
30
20
50
40
Fig. 11PV Curve at different power factors: I = 100 lead
International Science Index, Electrical and Computer Engineering Vol:2, No:6, 2008 waset.org/Publication/14898
U, kV
0.7
0.6
0.5
0.4
Fig. 8 The grid connection of the proposed Phuoc Ninh wind farm –
Viet Nam (2015)
0.3
0.2
In order to investigate the impact of the injection of active
power by the wind farm the system is approximated to a series
of impedances as indicated below.
0.1
P, MW
0
Wind farm
690 V
690 V
20
30
40
50
60
Fig. 12 PV Curve at different power factors: I = 200 lead
•
Z = 0,00125 +j0.005
10
•
Fig. 9 Equivalent grid and connection system impedance as seen
from the low voltage (690V)
U, kV
For this option the voltage profile at the generator terminals
is required and therefore all the impedances need to be
reflected to the voltage level at the generator, i.e. 690V.
Fundamentally, it simulates the injection of current from the
wind farm in steps and calculates the voltage dropped across
the Thévenin impedance at each step. This builds up number
of points for the voltage at the generator terminals as the
power injected increases. The resulting plotted curve is known
the voltage “nose” curve due to its shape.
The PV curves for the above problem has been drawn for
0°,10° leading and 20° leading power factor angle. From the
curve we obtain that value of PL increases from lagging to
leading power factor. We also obtain that there are two values
of UL for a given PL except at PLmax. The curves is shown in
figure 10 to 12.
0.7
0.6
0.5
0.4
0.3
0.2
0.1
P, MW
0
5
10
15
20
25
30
35
Fig. 10 PV Curve at different power factors: I = 00
40
This graph shows that, following the pf =1 (i.e. power factor
compensation so that it is corrected to unity power factor)
from left to right, the voltage rises as the current injected
increases and the power increases to about 39,03 MW. Then
after 39,03 MW the voltage starts to drop until the “nose”
point where the rate of decrease in voltage is faster than the
rate of increase in the current injected and the power actually
drops. This (the nose point) is the onset of voltage instability.
From this it can be seen that i) approximately a maximum of
39,03 MW power can be injected without instability, and ii)
reactive power control is necessary so that the wind farm can
be operated at, or very close to, unity power factor. If the
power factor drops, it can be seen that operation is much too
International Scholarly and Scientific Research & Innovation 2(6) 2008
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World Academy of Science, Engineering and Technology
International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering Vol:2, No:6, 2008
International Science Index, Electrical and Computer Engineering Vol:2, No:6, 2008 waset.org/Publication/14898
close to the point of voltage instability. Furthermore, the basic
compensation known as “no-load” compensation (i.e.
compensation for the reactive power drawn by the induction
machines when they are connected but not operating) is
insufficient. What all this means, in practice, is that if the
power factor compensation units fail then wind farm
production must be stopped.
VI. CONCLUSION
There is a need for WGs to be able to operate within a
voltage envelope to maximise dispatch of active power.
Additionally, at times when network voltage is depressed the
same system could export controlled reactive power for
system voltage support. Some Distribution Network Operator
are now prepared to consider and integrate WGs that can
operate to provide voltage support. Network reinforcement
costs may be deferred and loss of generation due to overvoltage shutdown may be reduced. Busbar, generator and
excitation system protection settings and timings will require
to be applied carefully, within statutory and manufacturers’
limits to ensure that WG plant operates within accepted
network voltages and machine ratings.
[8]
Poul Sørensen, Anca Hansen, Lorand Janosi, John Bech, Birgitte
Bak-Jensen; Simulation of Interaction between Wind Farm and Power
System; Risø National Laboratory, Roskilde December 2001.
[9] M. Chinchilla, S. Arnalte, J.C. Burgos, J.L. Rodrı´guez; Power limits
of grid-connected modern wind energy systems; Journal of Renewable
Energy 31 (2005) 1455–1470.
[10] Wind Energy Resource Atlas of Southeast Asia; WB 2001.
[11] Trinh Trong Chuong; An investigation into voltage and power relation
at the load bus to estimate voltage stability limit in distribution network
with wind generations; The First International Conference Sustainable
Energy Development, SED - 2008.
Trinh Trong Chuong was born in 1976 in
HaiDuong, Vietnam. He received the B.E. and M.E.
degrees in electrical power systems from Hanoi
University of Technology, Hanoi, Vietnam, in 1999
and in 2003. He is currently pursuing the Ph.D.
degree with the Department of Electric Power
system, Hanoi University of Technology. His
interests are distributed generation, voltage stability,
power quality, and optimal power flow.
Add:
Department: Electric Power System, Hanoi University of Industry; Minh Khai
village, TuLiem district, Hanoi, Vietnam. E-mail: chuonghtd@gmail.com
Simple analytical expression for real power critical voltage
has been formulated and had been used to draw PV curve of a
radial transmission line. It is observed that real power
increases from lagging to leading power factor. We also obtain
that there are two values of receiving end voltage UL for a
given PL except at PLmax. QV curves for fixed PL and different
UL can also be plotted using the derived relationship and
devised algorithm by varying reactive power.
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[2]
[3]
[4]
[5]
[6]
[7]
Trinh Trong Chuong; Voltage stability analysis of grid connected wind
generators; International Conference on Electrical Engineering;
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of Philosophi; Chalmers Unversity of Technology; Goteborg Swedent
2000.
McGraw-Edison Company, Power System Division: DistributionSystem Protection Manual.
Johannes Gerlof Slootweg; Wind Power: Modelling and Impact on
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Leuven, May 2006.
Feasibility Assessment and Capacity Building for Wind Energy
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